A new generation of fuel injection systems, in particular common-rail fuel injection systems, operates with directly driven piezo injectors actuating the nozzle needle via a hydraulic coupling element. In this context, the coupling element converts the translatory stroke of the piezo drive into a pressure differential which opens the nozzle needle. The coupling element comprises a piston and a pin which connects the piston to a piezo actuator. The piston is located in a pressure cylinder. When the piezo actuator extends, pressure is applied to fuel located in the pressure cylinder and under high pressure. This moves a nozzle needle to open an injection opening and fuel is thereby injected into a combustion chamber. Discharging the piezo actuator shortens its length, as a result of which the piston of the coupling element moves back and therefore brings about a reduction in pressure of the fuel, which reduction causes the nozzle needle to close the injection opening.
The transmission properties of such a coupling element are, apart from the physical characteristic variables of the fuel, dependent to a high degree on the leakage fluid that flows around the coupling element. A balance of inflowing, outflowing, and circulating quantities is established, which balance influences the respective dynamic transmission behavior and therefore the opening and closing of the needle. This balance changes as a function of temperature, viscosity, component tolerance, and aging, i.e., the gap cross section. To correct the actuation, it is useful to know the state of this balance. Known models find the temperature influence statistically by means of characteristic diagrams. However, until they do not detect the aging and component tolerance of such a hydraulic coupling element.